Abstract: The method for designing the pitch profile of a cam for a backingoff lathe was studied， with the Hermite return curve of the cam designed. The principle of machining the gear hob’s back surface using a backingoff lathe was outlined. The parametric equation of cubic Hermite return curve was proposed based on the differential geometry theory and Hermite polynomial interpolation combined with the curve boundary conditions. Taking the design of a backingoff cam as an example， the difference between the Archimedes return curve and Hermite one was compared and the influence of different types of return curves on machining process was analyzed， showing that the Hermite curve was better. To increase the design efficiency， the C language was used to program the pitch profile of the cam， and the opensource software package gnuplot and LaTeX were used to show the design graph.

Key words: cam, cam profile, return curve, Archimedes spiral, Hermite interpolation curve